Generic simplicity of resonances in obstacle scattering

Abstract

We show that all resonances in Dirichlet obstacle scattering (in $\mathbb{C}$ in odd dimensions and in the logarithmic cover of $\mathbb{C}\setminus \{0\}$ in even dimensions) are generically simple in the class of obstacles with $C^k$ (and $C^{\infty }$) boundaries, $k\ge 2$.

References in corpus (1)

• Restriction Bounds for the Free Resolvent and Resonances in Lossy Scattering

Cited by in corpus (1)

• Surrogate modeling of resonant behavior in scattering problems through adaptive rational approximation and sketching